For a known method (Verpackungsrundschau 33 (1982), No. 8, pages 47-50; European patent 0 045 389 B1), a container is formed by thermoforming the container sheet and then acting upon it with steam, which brings about the sterilization of the container sheet on the filling side. For this process, the back container sheet is cooled by the wall of the molding tool. The aluminum lid sheet is sterilized on both sides as it passes through a steam chamber. The sterilization of the container sheet, accomplished in this way, leaves something to be desired and does not exclude the dangers of re-infection. In the case of plastic lid sheets, the simultaneous action of steam on both sides leads to distortion phenomena. Furthermore, it is known that, for sterilization purposes, container sheet, before it is shaped, can be pulled through a hydrogen peroxide bath, which brings about the sterilization of the sheet on both sides (DE 30 28 208 A1).